# Finding Exact Value of Trig Expression

## Homework Statement

Find the exact value of each expression:
a) sec-1($$\sqrt{}2$$)
b) sin-1(1)

## Homework Equations

sec$$\theta$$=$$\stackrel{}{}1/cos\theta$$

## The Attempt at a Solution

I've never learned this, but I am really curious in how it is solved.
Is there a formula for this? Thanks!

## Answers and Replies

These are inverse functions so:

a. For what value of x does sec(x) = sqrt(2)

b. For what value of x does sin(x) = 1?

Mark44
Mentor

## Homework Statement

Find the exact value of each expression:
a) sec-1($$\sqrt{}2$$)
b) sin-1(1)

## Homework Equations

sec$$\theta$$=$$\stackrel{}{}1/cos\theta$$

## The Attempt at a Solution

I've never learned this, but I am really curious in how it is solved.
Is there a formula for this? Thanks!
Do you understand inverse functions?

IOW, x = f-1(y) <==> y = f(x)

For example, suppose you were asked to find cos-1(1/2).

Let y = cos-1(1/2).
That is equivalent to 1/2 = cos(y). What angle in the interval [0, $\pi$] has a cosine of 1/2?

Do you understand inverse functions?

IOW, x = f-1(y) <==> y = f(x)

For example, suppose you were asked to find cos-1(1/2).

Let y = cos-1(1/2).
That is equivalent to 1/2 = cos(y). What angle in the interval [0, $\pi$] has a cosine of 1/2?

Should I memorize the circle with all the angles?
And this may sound silly...but on (x,y), which is cos and sin? Is it like (cos, sin) on the circle, or the opposite?

Mark44
Mentor
On the unit circle, x = cos(t) and y = sin(t).

hunt_mat
Homework Helper
A simple way to look at the problem is let $$a=\sec^{-1}\sqrt{2}$$ then $$\sec a=\sqrt{2}$$. From here it is easy to compute the value a by turning sec into cos and using information about known values of cos.

Last edited:
Thank you all for the input! I think I will learn to memorize the circle with all the angles....I'm sure that will help.